1. ## How to prove this (about determinants)

honestly ive searched through the stickied posts (compilation of proofs) and some other threads, but i think i was just too blind to see it if this was already posted,

anyway, i was told that:
if a row/column of a matrix is a SCALAR MULTIPLE of another (in the same matrix)
then its det is 0,

hmm, i really tried this with some examples and its true,
can anyone prove this? i dont wanna present my answer without any proofs

2. Think of rules about interchanging, adding, subtracting rows/columns in a determinant. Then think of easy ways to calculate a determinant.

3. Originally Posted by experiment00
honestly ive searched through the stickied posts (compilation of proofs) and some other threads, but i think i was just too blind to see it if this was already posted,

anyway, i was told that:
if a row/column of a matrix is a SCALAR MULTIPLE of another (in the same matrix)
then its det is 0,

hmm, i really tried this with some examples and its true,
can anyone prove this? i dont wanna present my answer without any proofs
By performing a simple elementary row operation you can get a matrix with a row/column whose entries are all zero. This matrix will have the same determinant as the original. Therefore ....

4. i see!
so if make these rows/columns (the other one being a multiple of the other) equal by extracting the "scale" (lol dunno the term) XD
then negate one of these equal rows/columns, add both, viola!

thanks a lot sirs!